Ebook: Numerical Methods for Ordinary Differential Equations: Initial Value Problems
- Genre: Mathematics // Differential Equations
- Tags: Numerical Analysis, Numeric Computing
- Series: Springer Undergraduate Mathematics Series
- Year: 2010
- Publisher: Springer
- Edition: 1
- Language: English
- pdf
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.
It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.
Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.
The book covers key foundation topics:
o Taylor series methods
o Runge-Kutta methods
o Linear multistep methods
o Convergence
o Stability
and a range of modern themes:
o Adaptive stepsize selection
o Long term dynamics
o Modified equations
o Geometric integration
o Stochastic differential equations
The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.
It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.
Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.
The book covers key foundation topics:
o Taylor series methods
o Runge-Kutta methods
o Linear multistep methods
o Convergence
o Stability
and a range of modern themes:
o Adaptive stepsize selection
o Long term dynamics
o Modified equations
o Geometric integration
o Stochastic differential equations
The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.
It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.
Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.
The book covers key foundation topics:
o Taylor series methods
o Runge-Kutta methods
o Linear multistep methods
o Convergence
o Stability
and a range of modern themes:
o Adaptive stepsize selection
o Long term dynamics
o Modified equations
o Geometric integration
o Stochastic differential equations
The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Content:
Front Matter....Pages i-xiv
ODEs—An Introduction....Pages 1-18
Euler’s Method....Pages 19-31
The Taylor Series Method....Pages 33-42
Linear Multistep Methods—I: Construction and Consistency....Pages 43-60
Linear Multistep Methods—II: Convergence and Zero-Stability....Pages 61-73
Linear Multistep Methods—III: Absolute Stability....Pages 75-94
Linear Multistep Methods—IV: Systems of ODEs....Pages 95-108
Linear Multistep Methods—V: Solving Implicit Methods....Pages 109-121
Runge–Kutta Method—I: Order Conditions....Pages 123-134
Runge-Kutta Methods–II Absolute Stability....Pages 135-143
Adaptive Step Size Selection....Pages 145-163
Long-Term Dynamics....Pages 165-176
Modified Equations....Pages 177-193
Geometric Integration Part I—Invariants....Pages 195-206
Geometric Integration Part II—Hamiltonian Dynamics....Pages 207-223
Stochastic Differential Equations....Pages 225-241
Back Matter....Pages 243-271
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.
It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.
Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.
The book covers key foundation topics:
o Taylor series methods
o Runge-Kutta methods
o Linear multistep methods
o Convergence
o Stability
and a range of modern themes:
o Adaptive stepsize selection
o Long term dynamics
o Modified equations
o Geometric integration
o Stochastic differential equations
The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Content:
Front Matter....Pages i-xiv
ODEs—An Introduction....Pages 1-18
Euler’s Method....Pages 19-31
The Taylor Series Method....Pages 33-42
Linear Multistep Methods—I: Construction and Consistency....Pages 43-60
Linear Multistep Methods—II: Convergence and Zero-Stability....Pages 61-73
Linear Multistep Methods—III: Absolute Stability....Pages 75-94
Linear Multistep Methods—IV: Systems of ODEs....Pages 95-108
Linear Multistep Methods—V: Solving Implicit Methods....Pages 109-121
Runge–Kutta Method—I: Order Conditions....Pages 123-134
Runge-Kutta Methods–II Absolute Stability....Pages 135-143
Adaptive Step Size Selection....Pages 145-163
Long-Term Dynamics....Pages 165-176
Modified Equations....Pages 177-193
Geometric Integration Part I—Invariants....Pages 195-206
Geometric Integration Part II—Hamiltonian Dynamics....Pages 207-223
Stochastic Differential Equations....Pages 225-241
Back Matter....Pages 243-271
....